Adam J. Kucharski

Transmission Dynamics of Zika Virus in Island Populations: A Modelling Analysis of the 2013–14 French Polynesia Outbreak

Between October 2013 and April 2014, more than 30,000 cases of Zika virus (ZIKV) disease were estimated to have attended healthcare facilities in French Polynesia. ZIKV has also been reported in Africa and Asia, and in 2015 the virus spread to South America and the Caribbean. Infection with ZIKV has been associated with neurological complications including Guillain-Barré Syndrome (GBS) and microcephaly, which led the World Health Organization to declare a Public Health Emergency of International Concern in February 2015. To better understand the transmission dynamics of ZIKV, we used a mathematical model to examine the 2013–14 outbreak on the six major archipelagos of French Polynesia. Our median estimates for the basic reproduction number ranged from 2.6–4.8, with an estimated 11.5% (95% CI: 7.32–17.9%) of total infections reported. As a result, we estimated that 94% (95% CI: 91–97%) of the total population of the six archipelagos were infected during the outbreak. Based on the demography of French Polynesia, our results imply that if ZIKV infection provides complete protection against future infection, it would take 12–20 years before there are a sufficient number of susceptible individuals for ZIKV to re-emerge, which is on the same timescale as the circulation of dengue virus serotypes in the region. Our analysis suggests that ZIKV may exhibit similar dynamics to dengue virus in island populations, with transmission characterized by large, sporadic outbreaks with a high proportion of asymptomatic or unreported cases.

Potential for large outbreaks of Ebola virus disease

Highlights • We revisited data from the first known Ebola outbreak in Zaire in 1976.• Using a mathematical model, we estimated transmission rates in different settings.• Analysis suggests the person-to-person R0 was 1.34 (95% CI: 0.92–2.11).• Epidemiological conditions in 1976 could have generated a larger outbreak.

Case fatality rate for Ebola virus disease in west Africa

The case fatality rate (CFR) for the 2014 Ebola outbreak in west Africa has been widely reported to be much lower than for most previous outbreaks. However, this low rate is not necessarily a feature of the infection itself. Rather, it is likely to be the result of a failure to account for delays between disease onset and fi nal outcome. The low reported CFR values were generated from a so-called naive CFR calculation, in which the total number of deaths reported so far is divided by the total number of cases. Based on WHO reports up to Sept 7, 2014, which include 2226 deaths and 4390 cases, the naive CFR estimate is 51% (95% CI 49–53%). This naive approach does not account for the delay between onset of Ebola symptoms and disease outcome (ie, recovery or death). During the 1976 outbreak in Yambuku, Democratic Republic of the Congo, this delay was 7·5 days on average (appendix). In the middle of the outbreak, cases for which the outcome was as-yet unknown existed (appendix). Because the naive CFR calculation includes these cases—but not their outcomes—it generates a substantial underestimate of the actual CFR. Halfway through the 1976 outbreak, the naive CFR estimate would have been around 50%; as the outbreak reached its conclusion, this number would have climbed towards the much higher true value (fi gure). By contrast, if we only consider cases with known outcomes, the realtime estimate of CFR remains consistently high throughout. If cumulative incidences of cases and deaths are available, and delay from onset to outcome is known, the number of cases with outcomes can be estimated and hence a more accurate estimate of CFR obtained. We estimate that the 2014 infection has an overall CFR of around 70% at present using the 1976 distribution of Ebola onset to outcome and WHO reports on total cases and deaths across all countries in 2014. If the delay is longer than in 1976, this CFR could be even higher. The widely cited 2014 CFR of around 50% is therefore likely to be a substantial underestimate of the true value, and so the number could apparently rise over the course of the outbreak. With data on individual onsets and outcomes, more precise estimates of CFR could be obtained, and how it varies with setting and availability of treatment could be assessed.

Temporal Changes in Ebola Transmission in Sierra Leone and Implications for Control Requirements: a Real-time Modelling Study

Background: Between August and November 2014, the incidence of Ebola virus disease (EVD) rose dramatically in several districts of Sierra Leone. As a result, the number of cases exceeded the capacity of Ebola holding and treatment centres. During December, additional beds were introduced, and incidence declined in many areas. We aimed to measure patterns of transmission in different regions, and evaluate whether bed capacity is now sufficient to meet future demand. Methods: We used a mathematical model of EVD infection to estimate how the extent of transmission in the nine worst affected districts of Sierra Leone changed between 10th August 2014 and 18th January 2015. Using the model, we forecast the number of cases that could occur until the end of March 2015, and compared bed requirements with expected future capacity. Results: We found that the reproduction number, R, defined as the average number of secondary cases generated by a typical infectious individual, declined between August and December in all districts. We estimated that R was near the crucial control threshold value of 1 in December. We further estimated that bed capacity has lagged behind demand between August and December for most districts, but as a consequence of the decline in transmission, control measures caught up with the epidemic in early 2015. Conclusions: EVD incidence has exhibited substantial temporal and geographical variation in Sierra Leone, but our results suggest that the epidemic may have now peaked in Sierra Leone, and that current bed capacity appears to be sufficient to keep the epidemic under-control in most districts.

Measuring the impact of Ebola control measures in Sierra Leone.

Significance Between June 2014 and February 2015, thousands of Ebola treatment beds were introduced in Sierra Leone, alongside other infection control measures. However, there has been criticism of the timing and focus of this response, and it remains unclear how much it contributed to curbing the 2014–2015 Ebola epidemic. Using a mathematical model, we estimated how many Ebola virus disease cases the response averted in each district of Sierra Leone. We estimated that 56,600 (95% credible interval: 48,300–84,500) Ebola cases were averted in Sierra Leone as a direct result of additional treatment beds. Moreover, the number of cases averted would have been even greater had beds been available 1 month earlier. Between September 2014 and February 2015, the number of Ebola virus disease (EVD) cases reported in Sierra Leone declined in many districts. During this period, a major international response was put in place, with thousands of treatment beds introduced alongside other infection control measures. However, assessing the impact of the response is challenging, as several factors could have influenced the decline in infections, including behavior changes and other community interventions. We developed a mathematical model of EVD transmission, and measured how transmission changed over time in the 12 districts of Sierra Leone with sustained transmission between June 2014 and February 2015. We used the model to estimate how many cases were averted as a result of the introduction of additional treatment beds in each area. Examining epidemic dynamics at the district level, we estimated that 56,600 (95% credible interval: 48,300–84,500) Ebola cases (both reported and unreported) were averted in Sierra Leone up to February 2, 2015 as a direct result of additional treatment beds being introduced. We also found that if beds had been introduced 1 month earlier, a further 12,500 cases could have been averted. Our results suggest the unprecedented local and international response led to a substantial decline in EVD transmission during 2014–2015. In particular, the introduction of beds had a direct impact on reducing EVD cases in Sierra Leone, although the effect varied considerably between districts.

Estimating the Life Course of Influenza A(H3N2) Antibody Responses from Cross-Sectional Data

The immunity of a host population against specific influenza A strains can influence a number of important biological processes, from the emergence of new virus strains to the effectiveness of vaccination programmes. However, the development of an individual’s long-lived antibody response to influenza A over the course of a lifetime remains poorly understood. Accurately describing this immunological process requires a fundamental understanding of how the mechanisms of boosting and cross-reactivity respond to repeated infections. Establishing the contribution of such mechanisms to antibody titres remains challenging because the aggregate effect of immune responses over a lifetime are rarely observed directly. To uncover the aggregate effect of multiple influenza infections, we developed a mechanistic model capturing both past infections and subsequent antibody responses. We estimated parameters of the model using cross-sectional antibody titres to nine different strains spanning 40 years of circulation of influenza A(H3N2) in southern China. We found that “antigenic seniority” and quickly decaying cross-reactivity were important components of the immune response, suggesting that the order in which individuals were infected with influenza strains shaped observed neutralisation titres to a particular virus. We also obtained estimates of the frequency and age distribution of influenza infection, which indicate that although infections became less frequent as individuals progressed through childhood and young adulthood, they occurred at similar rates for individuals above age 30 y. By establishing what are likely to be important mechanisms driving epochal trends in population immunity, we also identified key directions for future studies. In particular, our results highlight the need for longitudinal samples that are tested against multiple historical strains. This could lead to a better understanding of how, over the course of a lifetime, fast, transient antibody dynamics combine with the longer-term immune responses considered here.

The role of superspreading in Middle East respiratory syndrome coronavirus (MERS-CoV) transmission.

As at 15 June 2015, a large transmission cluster of Middle East respiratory syndrome coronavirus (MERSCoV)was ongoing in South Korea. To examine the potential for such events, we estimated the level of heterogeneity in MERS-CoV transmission by analyzing data on cluster size distributions. We found substantial potential for superspreading; even though it is likely that R0 < 1 overall, our analysis indicates that cluster sizes of over 150 cases are not unexpected forMERS-CoV infection.

The contribution of social behaviour to the transmission of influenza A in a human population.

Variability in the risk of transmission for respiratory pathogens can result from several factors, including the intrinsic properties of the pathogen, the immune state of the host and the hosts behaviour. It has been proposed that self-reported social mixing patterns can explain the behavioural component of this variability, with simulated intervention studies based on these data used routinely to inform public health policy. However, in the absence of robust studies with biological endpoints for individuals, it is unclear how age and social behaviour contribute to infection risk. To examine how the structure and nature of social contacts influenced infection risk over the course of a single epidemic, we designed a flexible disease modelling framework: the population was divided into a series of increasingly detailed age and social contact classes, with the transmissibility of each age-contact class determined by the average contacts of that class. Fitting the models to serologically confirmed infection data from the 2009 Hong Kong influenza A/H1N1p pandemic, we found that an individuals risk of infection was influenced strongly by the average reported social mixing behaviour of their age group, rather than by their personal reported contacts. We also identified the resolution of social mixing that shaped transmission: epidemic dynamics were driven by intense contacts between children, a post-childhood drop in risky contacts and a subsequent rise in contacts for individuals aged 35–50. Our results demonstrate that self-reported social contact surveys can account for age-associated heterogeneity in the transmission of a respiratory pathogen in humans, and show robustly how these individual-level behaviours manifest themselves through assortative age groups. Our results suggest it is possible to profile the social structure of different populations and to use these aggregated data to predict their inherent transmission potential.

Effectiveness of Ring Vaccination as Control Strategy for Ebola Virus Disease.

Using an Ebola virus disease transmission model, we found that addition of ring vaccination at the outset of the West Africa epidemic might not have led to containment of this disease. However, in later stages of the epidemic or in outbreaks with less intense transmission or more effective control, this strategy could help eliminate the disease.

Comparative analysis of dengue and Zika outbreaks reveals differences by setting and virus

The pacific islands of Micronesia have experienced several outbreaks of mosquito-borne diseases over the past decade. In outbreaks on small islands, the susceptible population is usually well defined, and there is no co-circulation of pathogens. Because of this, analysing such outbreaks can be useful for understanding the transmission dynamics of the pathogens involved, and particularly so for yet understudied pathogens such as Zika virus. Here, we compared three outbreaks of dengue and Zika virus in two different island settings in Micronesia, the Yap Main Islands and Fais, using a mathematical model of transmission dynamics and making full use of commonalities in disease and setting between the outbreaks. We found that the estimated reproduction numbers for Zika and dengue were similar when considered in the same setting, but that, conversely, reproduction number for the same disease can vary considerably by setting. On the Yap Main Islands, we estimated a reproduction number of 8.0–16 (95% Credible Interval (CI)) for the dengue outbreak and 4.8–14 (95% CI) for the Zika outbreak, whereas for the dengue outbreak on Fais our estimate was 28–102 (95% CI). We further found that the proportion of cases of Zika reported was smaller (95% CI 1.4%–1.9%) than that of dengue (95% CI: 47%–61%). We confirmed these results in extensive sensitivity analysis. They suggest that models for dengue transmission can be useful for estimating the predicted dynamics of Zika transmission, but care must be taken when extrapolating findings from one setting to another.